{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font size=6>集成学习</font>\n",
    "# 概述\n",
    "## 原理\n",
    "集成学习(ensemble learning)可以说是现在非常火爆的机器学习方法了。它本身不是一个单独的机器学习算法，而是通过构建并结合多个机器学习器来完成学习任务。也就是我们常说的“博采众长”。集成学习可以用于分类问题集成，回归问题集成，特征选取集成，异常点检测集成等等，可以说所有的机器学习领域都可以看到集成学习的身影。\n",
    "\n",
    "**组成：**\n",
    "1. 若干个个体学习器\n",
    "2. 结合策略\n",
    "<img width=60% src=\"images/9113eb778da49f32c749dbc3c34fa412.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 个体学习器\n",
    "**两种个体学习器组合：**\n",
    "1. 同质个体学习器：所有的个体学习器都是一个种类的，或者说是同质的；\n",
    "    1. 个体学习串行\n",
    "    2. 个体学习并行\n",
    "2. 异质个体学习器：所有的个体学习器不全是一个种类的；\n",
    "\n",
    "### bagging\n",
    "bagging属于同质个体学习器，个体学习器之间没有依赖关系，并行组合。从训练集进行子抽样组成每个基模型所需要的子训练集，对所有基模型预测的结果进行综合产生最终的预测结果：\n",
    "<img src=\"images/9edf53941bf363de1fb186433cce6e28_hd.jpg\">\n",
    "\n",
    "**自助采样法（Bootstrap sampling）**\n",
    "\n",
    "自助法顾名思义，是这样一种方法：即从样本自身中再生成很多可用的同等规模的新样本，从自己中产生和自己类似的，所以叫做自助，即不借助其他样本数据。例如，对于m个样本的原始训练集，我们每次先随机采集一个样本放入采样集，接着把该样本放回，也就是说下次采样时该样本仍有可能被采集到，这样采集m次，最终可以得到m个样本的采样集，由于是随机采样，这样每次的采样集是和原始训练集不同的，和其他采样集也是不同的\n",
    "\n",
    "**随机森林**\n",
    "\n",
    "是bagging的一个特化进阶版，所谓的特化是因为随机森林的弱学习器都是决策树。所谓的进阶是随机森林在bagging的样本随机采样基础上，又加上了特征的随机选择，其基本思想没有脱离bagging的范畴。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### boosting\n",
    "boosting组合算法的训练过程为阶梯状，基模型（个体学习器）按次序一一进行训练（即串行，但是实现上可以做到并行），基模型的训练集按照某种策略每次都进行一定的转化。最后采用综合算法对所有基模型预测的结果进行综合产生最终的预测结果。\n",
    "<img src=\"images/10ebb74ac1a0c5bf03f890f3502c9095_hd.jpg\">\n",
    "\n",
    "Boosting系列算法里最著名算法主要有AdaBoost算法和提升树(boosting tree)系列算法。提升树系列算法里面应用最广泛的是梯度提升树(Gradient Boosting Decison Tree即GBDT)。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### stacking\n",
    "将训练好的所有基模型对训练集进行预测，第j个基模型对第i个训练样本的预测值将作为新的训练集中第i个样本的第j个特征值，最后基于新的训练集进行训练。同理，预测的过程也要先经过所有基模型的预测形成新的测试集，最后再对测试集进行预测。stacking算法在个体学习器可是同质的也可以是异质的，某种程度来说，stacking算法类似于支持向量机的核函数，起到对训练集做升维降维的作用。\n",
    "<img src=\"images/c0ab04181bfadb224e1b3cf058380de1_hd.jpg\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 结合策略\n",
    "假设我们得到了T个弱学习器（也叫个体学习器或基学习器），即$\\{h_1,h_2,...h_T\\}$\n",
    "### 平均法\n",
    "对于数值类的回归预测问题，通常使用的结合策略是平均法，即，对于若干个弱学习器的输出进行平均得到最终的预测输出。\n",
    "\n",
    "1. 最简单的平均是算术平均：$H(x) = \\frac{1}{T}\\sum\\limits_{1}^{T}h_i(x)$\n",
    "2. 如果每个个体学习器有一个权重w，则最终预测是$H(x) = \\sum\\limits_{i=1}^{T}w_ih_i(x),w_i \\geq 0 ,\\;\\;\\; \\sum\\limits_{i=1}^{T}w_i = 1$\n",
    "\n",
    "### 投票法\n",
    "对于分类问题的预测，我们通常使用的是投票法。假设我们的预测类别是$\\{c_1,c_2,...c_K\\}$，对于任意一个预测样本x，我们的$T$个弱学习器的预测结果分别是$(h_1(x), h_2(x)...h_T(x))$。\n",
    "1. 相对多数投票法，也就是$T$个弱学习器的对样本$x$的预测结果中，数量最多的类别$c_i$为最终的分类类别；\n",
    "2. 绝对多数投票法，即，在相对多数投票法的基础上，不光要求获得最高票，还要求票过半数。否则会拒绝预测；\n",
    "3. 加权投票法，和加权平均法一样，每个弱学习器的分类票数要乘以一个权重，最终将各个类别的加权票数求和，最大的值对应的类别为最终类别；\n",
    "\n",
    "### 学习法\n",
    "对于学习法，代表方法是stacking，当使用stacking的结合策略时， 我们不是对弱学习器的结果做简单的逻辑处理，而是再加上一层学习器，也就是说，我们将训练集弱学习器的学习结果作为输入，将训练集的输出作为输出，重新训练一个学习器来得到最终结果。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 随机森林\n",
    "随机森林是bagging算法中最常用的算法，它可以很方便的并行训练。\n",
    "## bagging算法流程\n",
    "输入为样本集：$D=\\{(x_,y_1),(x_2,y_2), ...(x_m,y_m)\\}$，弱学习器算法, 弱分类器迭代次数$T$。\n",
    "\n",
    "输出为最终的强分类器$f(x)$\n",
    "\n",
    "流程：\n",
    "1. 遍历$T$次：\n",
    "    1. 对训练集进行第$t$次自助采样，即，有放回的随机采样，共采集$m$次，得到包含$m$个样本的采样集$D_t$；\n",
    "    2. 用采样集$D_t$训练第$t$个弱学习器$G_t(x)$\n",
    "2. 综合策略：\n",
    "    1. 如果是分类算法预测，则$T$个弱学习器投出最多票数的类别或者类别之一为最终类别；\n",
    "    2. 如果是回归算法，$T$个弱学习器得到的回归结果进行算术平均得到的值为最终的模型输出。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 随机森林算法\n",
    "随机森林(Random Forest,简称RF)是bagging算法的进化版，进化体现如下：\n",
    "1. RF使用了CART决策树作为弱学习器；\n",
    "2. RF对决策树的建立做了改进。对于普通的决策树，我们会在节点上所有的$n$个样本特征中选择一个最优的特征来做决策树的左右子树划分，但是RF通过随机选择节点上的一部分样本特征，这个数字小于$n$，假设为$n_{sub}$，然后在这些随机选择的$n_{sub}$个样本特征中，选择一个最优的特征来做决策树的左右子树划分。这样进一步增强了模型的泛化能力。\n",
    "\n",
    "**算法流程：**\n",
    "\n",
    "输入为样本集：$D=\\{(x_,y_1),(x_2,y_2), ...(x_m,y_m)\\}$~~，<font color=\"red\">弱学习器算法</font>~~, 弱分类器迭代次数$T$。\n",
    "\n",
    "输出为最终的强分类器$f(x)$\n",
    "\n",
    "流程：\n",
    "1. 遍历$T$次：\n",
    "    1. 对训练集进行第$t$次自助采样，即，有放回的随机采样，共采集$m$次，得到包含$m$个样本的采样集$D_t$；\n",
    "    2. 用采样集$D_t$训练第$t$个弱学习器$G_t(x)$，<font color=\"red\">在训练决策树模型的节点的时候， 在节点上所有的样本特征中选择一部分样本特征， 在这些随机选择的部分样本特征中选择一个最优的特征来做决策树的左右子树划分</font>；\n",
    "2. 综合策略：\n",
    "    1. 如果是分类算法预测，则$T$个弱学习器投出最多票数的类别或者类别之一为最终类别；\n",
    "    2. 如果是回归算法，$T$个弱学习器得到的回归结果进行算术平均得到的值为最终的模型输出。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 随机森林总结\n",
    "优点：\n",
    "1. 训练可以高度并行化；\n",
    "2. 由于可以随机选择决策树节点划分特征，这样在样本特征维度很高的时候，仍然能高效的训练模型；\n",
    "3. 在训练后，可以给出各个特征对于输出的重要性；\n",
    "4. 由于采用了随机采样，训练出的模型的方差小，泛化能力强。\n",
    "6. 对部分特征缺失不敏感。\n",
    "\n",
    "缺点：\n",
    "1. 在某些噪音比较大的样本集上，RF模型容易陷入过拟合。\n",
    "2. 取值划分比较多的特征容易对RF的决策产生更大的影响，从而影响拟合的模型的效果。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## scikit-learn随机森林类库\n",
    "在scikit-learn中，RF的分类类是RandomForestClassifier，回归类是RandomForestRegressor。\n",
    "\n",
    "RF需要调参的参数包括两部分，第一部分是Bagging框架的参数，第二部分是CART决策树的参数。\n",
    "### RF框架参数\n",
    "1. n_estimators: 也就是弱学习器的最大迭代次数，或者说最大的弱学习器的个数。一般来说n_estimators太小，容易欠拟合，n_estimators太大，计算量会太大，并且n_estimators到一定的数量后，再增大n_estimators获得的模型提升会很小，所以一般选择一个适中的数值。默认是100。\n",
    "2. oob_score :即是否采用袋外样本来评估模型的好坏。默认识False。推荐设置为True，因为袋外分数反应了一个模型拟合后的泛化能力。\n",
    "3. criterion: 即CART树做划分时对特征的评价标准。分类模型和回归模型的损失函数是不一样的。分类RF对应的CART分类树默认是基尼系数gini,另一个可选择的标准是信息增益。回归RF对应的CART回归树默认是均方差mse，另一个可以选择的标准是绝对值差mae。一般来说选择默认的标准就已经很好的。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### RF决策树参数\n",
    "1. RF划分时考虑的最大特征数max_features。\n",
    "2. 决策树最大深度max_depth。\n",
    "3. 内部节点再划分所需最小样本数min_samples_split。\n",
    "4. 叶子节点最少样本数min_samples_leaf。\n",
    "5. 叶子节点最小的样本权重和min_weight_fraction_leaf。\n",
    "6. 最大叶子节点数max_leaf_nodes。\n",
    "7. 节点划分最小不纯度min_impurity_split。\n",
    "\n",
    "上面决策树参数中最重要的包括最大特征数max_features， 最大深度max_depth， 内部节点再划分所需最小样本数min_samples_split和叶子节点最少样本数min_samples_leaf。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 案例\n",
    "### 分类等高线"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import  datasets\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x288175f1898>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_moons\n",
    "X, y = make_moons(n_samples=1000,noise=.2)\n",
    "def make_meshgrid(x, y, h=.02):\n",
    "    \"\"\"\n",
    "    根据特征向量，和网格间距参数，绘制网格点阵图\n",
    "    \"\"\"\n",
    "    x_min, x_max = x.min() - 1, x.max() + 1\n",
    "    y_min, y_max = y.min() - 1, y.max() + 1\n",
    "    xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\n",
    "                         np.arange(y_min, y_max, h))\n",
    "    return xx, yy\n",
    "def plot_contours(ax, clf, xx, yy, **params):\n",
    "    \"\"\"绘制决策边界.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    ax: 绘图对象\n",
    "    clf: 分类模型\n",
    "    xx: 特征数据点\n",
    "    yy: 特征数据点\n",
    "    params: 字典参数\n",
    "    \"\"\"\n",
    "    Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "    Z = Z.reshape(xx.shape)\n",
    "    out = ax.contourf(xx, yy, Z, **params)\n",
    "    return out\n",
    "X0, X1 = X[:, 0], X[:, 1]\n",
    "plot_contours(plt,RandomForestClassifier(n_estimators=20).fit(X,y),*make_meshgrid(X0,X1),cmap=plt.cm.coolwarm, alpha=0.8)\n",
    "plt.scatter(X0, X1,c=y, cmap=plt.cm.coolwarm, s=20, edgecolors='k')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 参数网格寻优"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GridSearchCV(cv=5, error_score='raise-deprecating',\n",
       "             estimator=RandomForestClassifier(bootstrap=True, class_weight=None,\n",
       "                                              criterion='gini', max_depth=None,\n",
       "                                              max_features='auto',\n",
       "                                              max_leaf_nodes=None,\n",
       "                                              min_impurity_decrease=0.0,\n",
       "                                              min_impurity_split=None,\n",
       "                                              min_samples_leaf=1,\n",
       "                                              min_samples_split=2,\n",
       "                                              min_weight_fraction_leaf=0.0,\n",
       "                                              n_estimators='warn', n_jobs=None,\n",
       "                                              oob_score=False,\n",
       "                                              random_state=None, verbose=0,\n",
       "                                              warm_start=False),\n",
       "             iid='warn', n_jobs=None,\n",
       "             param_grid={'n_estimators': range(10, 101, 10)},\n",
       "             pre_dispatch='2*n_jobs', refit=True, return_train_score=False,\n",
       "             scoring='roc_auc', verbose=0)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.model_selection import GridSearchCV\n",
    "gs=GridSearchCV(estimator=RandomForestClassifier(\n",
    "#                                                 min_samples_split=100\n",
    "#                                                 ,min_samples_leaf=20\n",
    "#                                                 ,max_depth=8\n",
    "#                                                 ,oob_score=True\n",
    "                                                )\n",
    "                ,param_grid={\"n_estimators\":range(10,101,10)}\n",
    "               ,scoring=\"roc_auc\"\n",
    "               ,cv=5)\n",
    "gs.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "({'n_estimators': 100}, 0.9924399999999999)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gs.best_params_,gs.best_score_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Adaboost\n",
    "boosting系列算法中， Adaboost是最著名的算法之一。Adaboost既可以用作分类，也可以用作回归。\n",
    "\n",
    "关键点：\n",
    "1. 计算学习误差率$e$；\n",
    "2. 计算弱学习器权重系数$α$；\n",
    "3. 更新样本权重$D$；\n",
    "4. 确定结合策略；\n",
    "<img src=\"images/10ebb74ac1a0c5bf03f890f3502c9095_hd.jpg\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Adaboost算法的基本思路\n",
    "假设我们的训练集样本是$T=\\{(x_,y_1),(x_2,y_2), ...(x_m,y_m)\\}$,训练集的在第k个弱学习器的输出权重为$D(k) = (w_{k1}, w_{k2}, ...w_{km}) ;\\;\\; w_{1i}=\\frac{1}{m};\\;\\; i =1,2...m$\n",
    "### 分类问题\n",
    "#### 误差率\n",
    "分类问题的误差率很好理解和计算。由于多元分类是二元分类的推广，这里假设我们是二元分类问题，输出为{-1，1}，则第k个弱分类器$G_k(x)$在训练集上的加权误差率为$e_k = P(G_k(x_i) \\neq y_i) = \\sum\\limits_{i=1}^{m}w_{ki}I(G_k(x_i) \\neq y_i)$\n",
    "#### 弱学习器权重系数\n",
    "对于二元分类问题，第k个弱分类器$G_k(x)$的权重系数为$\\alpha_k = \\frac{1}{2}log\\frac{1-e_k}{e_k}$。\n",
    "\n",
    "从上式可以看出，如果分类误差率$e_k$越大，则对应的弱分类器权重系数$\\alpha_k$越小。也就是说，误差率小的弱分类器权重系数越大。\n",
    "#### 更新样本权重D\n",
    "假设第k个弱分类器的样本集权重系数为$D(k) = (w_{k1}, w_{k2}, ...w_{km})$，则对应的第k+1个弱分类器的样本集权重系数为$$w_{k+1,i} = \\frac{w_{ki}}{Z_K}exp(-\\alpha_ky_iG_k(x_i))$$\n",
    "这里$Z_k$是规范化因子$$Z_k = \\sum\\limits_{i=1}^{m}w_{ki}exp(-\\alpha_ky_iG_k(x_i))$$\n",
    "\n",
    "从$w_{k+1}$计算公式可以看出，如果第i个样本分类错误，则$y_iG_k(x_i) < 0$,导致样本的权重在第k+1个弱分类器中增大，如果分类正确，则权重在第k+1个弱分类器中减少。\n",
    "#### 结合策略\n",
    "Adaboost分类采用的是加权表决法。\n",
    "### 回归问题\n",
    "#### 误差率\n",
    "对于第k个弱学习器，计算他在训练集上的最大误差$$E_k= max|y_i - G_k(x_i)|\\;i=1,2...m$$\n",
    "然后计算每个样本的相对误差$$e_{ki}= \\frac{|y_i - G_k(x_i)|}{E_k}$$\n",
    "这里是误差损失为线性时的情况，如果我们用平方误差，则$$e_{ki}= \\frac{(y_i - G_k(x_i))^2}{E_k^2}$$，如果我们用的是指数误差，则$$e_{ki}= 1 - exp（\\frac{-y_i + G_k(x_i))}{E_k}）$$\n",
    "最终得到第k个弱学习器的 误差率$$e_k =  \\sum\\limits_{i=1}^{m}w_{ki}e_{ki}$$\n",
    "#### 弱学习器权重系数\n",
    "$$\\alpha_k =\\frac{e_k}{1-e_k}$$\n",
    "\n",
    "#### 更新样本权重D\n",
    "$$w_{k+1,i} = \\frac{w_{ki}}{Z_k}\\alpha_k^{1-e_{ki}}$$\n",
    "规范化因子$$Z_k = \\sum\\limits_{i=1}^{m}w_{ki}\\alpha_k^{1-e_{ki}}$$\n",
    "\n",
    "#### 结合策略\n",
    "加权的弱学习器取权重中位数对应的弱学习器作为强学习器的方法"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## AdaBoost分类问题的损失函数优化\n",
    "算法是通过一轮轮的弱学习器学习，利用前一个弱学习器的结果来更新后一个弱学习器的训练集权重。也就是说，第k-1轮的强学习器为$$f_{k-1}(x) = \\sum\\limits_{i=1}^{k-1}\\alpha_iG_{i}(x)$$而第k轮的强学习器为$$f_{k}(x) = \\sum\\limits_{i=1}^{k}\\alpha_iG_{i}(x)$$综合可以得到$$f_{k}(x) = f_{k-1}(x) + \\alpha_kG_k(x)$$\n",
    "\n",
    "Adaboost损失函数为指数函数，即定义损失函数为$$\\underbrace{arg\\;min\\;}_{\\alpha, G} \\sum\\limits_{i=1}^{m}exp(-y_if_{k}(x))$$,综合上式可得损失函数为$$(\\alpha_k, G_k(x)) = \\underbrace{arg\\;min\\;}_{\\alpha, G}\\sum\\limits_{i=1}^{m}exp[(-y_i) (f_{k-1}(x) + \\alpha G(x))]$$\n",
    "\n",
    "令$w_{ki}^{’} = exp(-y_if_{k-1}(x))$，它的值不依赖于$\\alpha, G$，因此与最小化无关，仅仅依赖于$f_{k-1}(x)$，随着每一轮迭代而改变。\n",
    "\n",
    "将这个式子带入损失函数,损失函数转化为$$(\\alpha_k, G_k(x)) = \\underbrace{arg\\;min\\;}_{\\alpha, G}\\sum\\limits_{i=1}^{m}w_{ki}^{’}exp[-y_i\\alpha G(x)]$$\n",
    "\n",
    "首先，我们求$G_k(x)$，可以得到$$G_k(x) = \\underbrace{arg\\;min\\;}_{G}\\sum\\limits_{i=1}^{m}w_{ki}^{’}I(y_i \\neq G(x_i))$$\n",
    "将$G_k(x)$带入损失函数，并对$\\alpha$求导,使其等于0，则就得到了$$\\alpha_k = \\frac{1}{2}log\\frac{1-e_k}{e_k}$$其中，$e_k$即为我们前面的分类误差率。$$e_k = \\frac{\\sum\\limits_{i=1}^{m}w_{ki}^{’}I(y_i \\neq G(x_i))}{\\sum\\limits_{i=1}^{m}w_{ki}^{’}} = \\sum\\limits_{i=1}^{m}w_{ki}I(y_i \\neq G(x_i))$$\n",
    "\n",
    "最后看样本权重的更新。利用$$f_{k}(x) = f_{k-1}(x) + \\alpha_kG_k(x)$$和$$w_{ki}^{’} = exp(-y_if_{k-1}(x))$$即可得：$$w_{k+1,i}^{’} = w_{ki}^{’}exp[-y_i\\alpha_kG_k(x)]$$这样就得到了我们的样本权重更新公式。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## AdaBoost二元分类问题算法流程\n",
    "输入为样本集$T=\\{(x_,y_1),(x_2,y_2), ...(x_m,y_m)\\}$，输出为{-1, +1}，弱分类器算法, 弱分类器迭代次数K\n",
    "\n",
    "输出为最终的强分类器$f(x)$\n",
    "\n",
    "1. 初始化样本集权重为$$D(1) = (w_{11}, w_{12}, ...w_{1m}) ;\\;\\; w_{1i}=\\frac{1}{m};\\;\\; i =1,2...m$$\n",
    "2. 迭代K次：\n",
    "    1. 使用具有权重$D_k$的样本集来训练数据，得到弱分类器$G_k(x)$\n",
    "    2. 计算$G_k(x)$的分类误差率$$e_k = P(G_k(x_i) \\neq y_i) = \\sum\\limits_{i=1}^{m}w_{ki}I(G_k(x_i) \\neq y_i)$$\n",
    "    3. 计算弱分类器的系数$$\\alpha_k = \\frac{1}{2}log\\frac{1-e_k}{e_k}$$\n",
    "    4. 更新样本集的权重分布$$w_{k+1,i} = \\frac{w_{ki}}{Z_K}exp(-\\alpha_ky_iG_k(x_i)) \\;\\; i =1,2,...m$$,规范化因子,$$Z_k = \\sum\\limits_{i=1}^{m}w_{ki}exp(-\\alpha_ky_iG_k(x_i))$$\n",
    "3. 构建最终分类器\n",
    "    \n",
    "对于Adaboost多元分类算法，其实原理和二元分类类似，最主要区别在弱分类器的系数上。比如Adaboost SAMME算法，它的弱分类器的系数$$\\alpha_k = \\frac{1}{2}log\\frac{1-e_k}{e_k} + log(R-1)$$，其中R为类别数。从上式可以看出，如果是二元分类，R=2，则上式和我们的二元分类算法中的弱分类器的系数一致。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Adaboost回归问题的算法流程\n",
    "输入为样本集$T=\\{(x_,y_1),(x_2,y_2), ...(x_m,y_m)\\}$，弱分类器算法, 弱分类器迭代次数K\n",
    "\n",
    "输出为最终的强分类器$f(x)$\n",
    "\n",
    "1. 初始化样本集权重为$$D(1) = (w_{11}, w_{12}, ...w_{1m}) ;\\;\\; w_{1i}=\\frac{1}{m};\\;\\; i =1,2...m$$\n",
    "2. 迭代K次：\n",
    "    1. 使用具有权重$D_k$的样本集来训练数据，得到弱分类器$G_k(x)$\n",
    "    2. 计算训练集上的最大误差$$E_k= max|y_i - G_k(x_i)|\\;i=1,2...m$$\n",
    "    3. 计算每个样本的相对误差:\n",
    "        1. 如果是线性误差，则$e_{ki}= \\frac{|y_i - G_k(x_i)|}{E_k}$;\n",
    "        2. 如果是平方误差，则$e_{ki}= \\frac{(y_i - G_k(x_i))^2}{E_k^2}$\n",
    "        3. 如果是指数误差，则$e_{ki}= 1 - exp（\\frac{-|y_i -G_k(x_i)|}{E_k}）$\n",
    "    4. 计算回归误差率$$e_k =  \\sum\\limits_{i=1}^{m}w_{ki}e_{ki}$$\n",
    "    5. 计算弱学习器的系数$$\\alpha_k =\\frac{e_k}{1-e_k}$$\n",
    "    6. 更新样本集的权重分布为$$w_{k+1,i} = \\frac{w_{ki}}{Z_k}\\alpha_k^{1-e_{ki}}$$，规范化因子，$$Z_k = \\sum\\limits_{i=1}^{m}w_{ki}\\alpha_k^{1-e_{ki}}$$\n",
    "3. 构建最终强学习器"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Adaboost算法的正则化\n",
    "为了防止Adaboost过拟合，我们通常也会加入正则化项，这个正则化项我们通常称为步长(learning rate)。定义为$ν$,对于前面的弱学习器的迭代$$f_{k}(x) = f_{k-1}(x) + \\alpha_kG_k(x)$$如果我们加上了正则化项，则有$$f_{k}(x) = f_{k-1}(x) + \\nu\\alpha_kG_k(x)$$$ν$的取值范围为$0<ν≤1$。对于同样的训练集学习效果，较小的$ν$意味着我们需要更多的弱学习器的迭代次数。通常我们用步长和迭代最大次数一起来决定算法的拟合效果。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Adaboost总结\n",
    "优点：\n",
    "1. Adaboost作为分类器时，分类精度很高\n",
    "2. 在Adaboost的框架下，可以使用各种回归分类模型来构建弱学习器，非常灵活。\n",
    "3. 作为简单的二元分类器时，构造简单，结果可理解。\n",
    "4. 不容易发生过拟合\n",
    "\n",
    "缺点：\n",
    "\n",
    "1. 对异常样本敏感，异常样本在迭代中可能会获得较高的权重，影响最终的强学习器的预测准确性。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## scikit-learn的Adaboost类库\n",
    "1. AdaBoostClassifier\n",
    "2. AdaBoostRegressor\n",
    "\n",
    "### 框架参数\n",
    "1. base_estimator：弱学习器；\n",
    "2. algorithm：这个参数只有AdaBoostClassifier有。SAMME和SAMME.R；\n",
    "3. loss：这个参数只有AdaBoostRegressor有，用于计算误差率。有线性‘linear’, 平方‘square’和指数 ‘exponential’三种选择, 默认是线性，一般使用线性就足够了，除非你怀疑这个参数导致拟合程度不好；\n",
    "4. n_estimators：弱学习器的最大迭代次数，或者说最大的弱学习器的个数；\n",
    "5. learning_rate:每个弱学习器的权重缩减系数$ν$,见$f_{k}(x) = f_{k-1}(x) + \\nu\\alpha_kG_k(x)$\n",
    "\n",
    "### 弱学习器参数\n",
    "见具体的若学习器，例如：CART分类树DecisionTreeClassifier和CART回归树DecisionTreeRegressor\n",
    "1. max_features；\n",
    "2. max_depth；\n",
    "3. min_samples_split；\n",
    "4. min_samples_leaf;\n",
    "5. min_weight_fraction_leaf;\n",
    "6. max_leaf_nodes;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 案例"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from sklearn.ensemble import AdaBoostClassifier\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.datasets import make_gaussian_quantiles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 生成2维正态分布，生成的数据按分位数分为两类，500个样本,2个样本特征，协方差系数为2\n",
    "X1, y1 = make_gaussian_quantiles(cov=2.0,n_samples=500, n_features=2,n_classes=2, random_state=1)\n",
    "# 生成2维正态分布，生成的数据按分位数分为两类，400个样本,2个样本特征均值都为3，协方差系数为2\n",
    "X2, y2 = make_gaussian_quantiles(mean=(3, 3), cov=1.5,n_samples=400, n_features=2, n_classes=2, random_state=1)\n",
    "#讲两组数据合成一组数据\n",
    "X = np.concatenate((X1, X2))\n",
    "y = np.concatenate((y1, - y2 + 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x28817719588>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], marker='o', c=y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AdaBoostClassifier(algorithm='SAMME',\n",
       "                   base_estimator=DecisionTreeClassifier(class_weight=None,\n",
       "                                                         criterion='gini',\n",
       "                                                         max_depth=2,\n",
       "                                                         max_features=None,\n",
       "                                                         max_leaf_nodes=None,\n",
       "                                                         min_impurity_decrease=0.0,\n",
       "                                                         min_impurity_split=None,\n",
       "                                                         min_samples_leaf=5,\n",
       "                                                         min_samples_split=20,\n",
       "                                                         min_weight_fraction_leaf=0.0,\n",
       "                                                         presort=False,\n",
       "                                                         random_state=None,\n",
       "                                                         splitter='best'),\n",
       "                   learning_rate=0.8, n_estimators=200, random_state=None)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bdt = AdaBoostClassifier(DecisionTreeClassifier(max_depth=2, min_samples_split=20, min_samples_leaf=5),\n",
    "                         algorithm=\"SAMME\",\n",
    "                         n_estimators=200, learning_rate=0.8)\n",
    "bdt.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1\n",
    "y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.02),\n",
    "                     np.arange(y_min, y_max, 0.02))\n",
    "\n",
    "Z = bdt.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "Z = Z.reshape(xx.shape)\n",
    "cs = plt.contourf(xx, yy, Z, cmap=plt.cm.Paired)\n",
    "plt.scatter(X[:, 0], X[:, 1], marker='o', c=y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Score: 0.9133333333333333\n"
     ]
    }
   ],
   "source": [
    "print(\"Score:\", bdt.score(X,y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Score: 0.9622222222222222\n"
     ]
    }
   ],
   "source": [
    "bdt = AdaBoostClassifier(DecisionTreeClassifier(max_depth=2, min_samples_split=20, min_samples_leaf=5),\n",
    "                         algorithm=\"SAMME\",\n",
    "                         n_estimators=300, learning_rate=0.8)\n",
    "bdt.fit(X, y)\n",
    "print(\"Score:\", bdt.score(X,y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Score: 0.8944444444444445\n"
     ]
    }
   ],
   "source": [
    "bdt = AdaBoostClassifier(DecisionTreeClassifier(max_depth=2, min_samples_split=20, min_samples_leaf=5),\n",
    "                         algorithm=\"SAMME\",\n",
    "                         n_estimators=300, learning_rate=0.5)\n",
    "bdt.fit(X, y)\n",
    "print(\"Score:\", bdt.score(X,y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Score: 0.9611111111111111\n"
     ]
    }
   ],
   "source": [
    "bdt = AdaBoostClassifier(DecisionTreeClassifier(max_depth=2, min_samples_split=20, min_samples_leaf=5),\n",
    "                         algorithm=\"SAMME\",\n",
    "                         n_estimators=600, learning_rate=0.7)\n",
    "bdt.fit(X, y)\n",
    "print(\"Score:\", bdt.score(X,y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# GBDT\n",
    "## 概述\n",
    "梯度提升树(Gradient Boosting Decison Tree, 以下简称GBDT)也是集成学习Boosting家族的成员，但是却和传统的Adaboost有很大的不同。Adaboost，是利用前一轮迭代弱学习器的误差率来更新训练集的权重，这样一轮轮的迭代下去。GBDT也是迭代，但是使用了前向分布算法，弱学习器限定了只能使用CART回归树模型，同时迭代思路和Adaboost也有所不同。\n",
    "\n",
    "在GBDT的迭代中，假设我们前一轮迭代得到的强学习器是$f_{t-1}(x)$，损失函数是$L(y, f_{t-1}(x))$，本轮迭代的目的是找到一个CART回归树模型的弱学习器$h_t(x)$，让本轮的损失函数$L(y, f_{t}(x)) =L(y, f_{t-1}(x)+ h_t(x))$最小。也就是说，本轮迭代找到决策树，要让样本的损失尽量变得更小。\n",
    "<img src=\"images/v2-55cee3e8fa13348b316543b50093d91f_b.jpg\">\n",
    "GBDT的思想可以用一个通俗的例子解释，假如有个人30岁，我们首先用20岁去拟合，发现损失有10岁，这时我们用6岁去拟合剩下的损失，发现差距还有4岁，第三轮我们用3岁拟合剩下的差距，差距就只有一岁了。如果我们的迭代轮数还没有完，可以继续迭代下面，每一轮迭代，拟合的岁数误差都会减小。\n",
    "## 算法流程\n",
    "<img src=\"images/equation.svg\">\n",
    "\n",
    "## 常用损失函数\n",
    "### 分类算法\n",
    "1. 如果是指数损失函数，则损失函数表达式为$L(y, f(x)) = exp(-yf(x))$\n",
    "2. 如果是对数损失函数:\n",
    "    1. 二元分类：$L(y, f(x)) = log(1+ exp(-yf(x)))$\n",
    "    2. 多元分类：$L(y, f(x)) = -  \\sum\\limits_{k=1}^{K}y_klog\\;p_k(x)$\n",
    "    \n",
    "### 回归算法\n",
    "1. 均方差:$L(y, f(x)) =(y-f(x))^2$;\n",
    "2. 绝对损失:$L(y, f(x)) =|y-f(x)|$;\n",
    "3. Huber损失,它是均方差和绝对损失的折衷产物，对于远离中心的异常点，采用绝对损失，而中心附近的点采用均方差。这个界限一般用分位数点度量。损失函数如下：$L(y, f(x))= \\begin{cases} \\frac{1}{2}(y-f(x))^2& {|y-f(x)| \\leq \\delta}\\\\ \\delta(|y-f(x)| - \\frac{\\delta}{2})& {|y-f(x)| > \\delta} \\end{cases}$;\n",
    "4. 分位数损失,它对应的是分位数回归的损失函数，表达式为$L(y, f(x)) =\\sum\\limits_{y \\geq f(x)}\\theta|y - f(x)| + \\sum\\limits_{y < f(x)}(1-\\theta)|y - f(x)|$\n",
    "\n",
    "Huber损失和分位数损失，主要用于健壮回归，也就是减少异常点对损失函数的影响。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 正则化\n",
    "和Adaboost一样，我们也需要对GBDT进行正则化，防止过拟合。GBDT的正则化主要有三种方式。\n",
    "\n",
    "第一种是和Adaboost类似的正则化项，即步长(learning rate)。定义为$ν$,对于前面的弱学习器的迭代$$f_{k}(x) = f_{k-1}(x) + h_k(x)$$如果我们加上了正则化项，则有$$f_{k}(x) = f_{k-1}(x) + \\nu h_k(x)$$\n",
    "\n",
    "$ν$的取值范围为$0<ν≤1$。对于同样的训练集学习效果，较小的$ν$意味着我们需要更多的弱学习器的迭代次数。通常我们用步长和迭代最大次数一起来决定算法的拟合效果。\n",
    "\n",
    "第二种正则化的方式是通过子采样比例（subsample）。取值为(0,1]。**这里的子采样和随机森林不一样，随机森林使用的是放回抽样，而这里是不放回抽样。**如果取值为1，则全部样本都使用，等于没有使用子采样。如果取值小于1，则只有一部分样本会去做GBDT的决策树拟合。选择小于1的比例可以减少方差，即防止过拟合，但是会增加样本拟合的偏差，因此取值不能太低。推荐在[0.5, 0.8]之间。\n",
    "\n",
    "使用了子采样的GBDT有时也称作随机梯度提升树(Stochastic Gradient Boosting Tree, SGBT)。由于使用了子采样，程序可以通过采样分发到不同的任务去做boosting的迭代过程，最后形成新树，从而减少弱学习器难以并行学习的弱点。\n",
    "\n",
    "第三种是对于弱学习器即CART回归树进行正则化剪枝。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## GBDT小结\n",
    "优点：\n",
    "1.  可以灵活处理各种类型的数据，包括连续值和离散值。\n",
    "2.  相对SVM来说,在相对少的调参时间情况下，预测的准确率也可以比较高。\n",
    "3.  使用一些健壮的损失函数，对异常值的鲁棒性非常强。如 Huber损失函数和Quantile损失函数。\n",
    "\n",
    "缺点:\n",
    "1. 弱学习器之间存在依赖关系，难以并行训练数据(不过可以通过自采样的SGBT来达到部分并行)。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## scikit-learn中的GBDT类库\n",
    "### 概述\n",
    "1. GradientBoostingClassifier；\n",
    "2. GradientBoostingRegressor；\n",
    "\n",
    "### 框架参数\n",
    "1. n_estimators: 也就是弱学习器的最大迭代次数，或者说最大的弱学习器的个数。\n",
    "2. learning_rate: 即每个弱学习器的权重缩减系数$ν$，也称作步长.\n",
    "3. subsample：取值为(0,1]。选择小于1的比例可以减少方差，即防止过拟合，但是会增加样本拟合的偏差，因此取值不能太低。推荐在[0.5, 0.8]之间，默认是1.0，即不使用子采样。\n",
    "4. init: 即我们的初始化的时候的弱学习器$f_0(x)$，如果不输入，则用训练集样本来做样本集的初始化分类回归预测。否则用init参数提供的学习器做初始化分类回归预测。\n",
    "5. loss: 即我们GBDT算法中的损失函数。对于分类模型，有对数似然损失函数\"deviance\"和指数损失函数\"exponential\"两者输入选择。默认是对数似然损失函数\"deviance\"。对于回归模型，有均方差\"ls\", 绝对损失\"lad\", Huber损失\"huber\"和分位数损失“quantile”。默认是均方差\"ls\"。\n",
    "6. alpha：这个参数只有GradientBoostingRegressor有，当我们使用Huber损失\"huber\"和分位数损失“quantile”时，需要指定分位数的值。默认是0.9，如果噪音点较多，可以适当降低这个分位数的值。\n",
    "\n",
    "### 弱学习器参数\n",
    "GBDT使用了CART回归决策树，因此它的参数基本来源于决策树类."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 案例"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x28818cf8048>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], marker='o', c=y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GradientBoostingClassifier(criterion='friedman_mse', init=None,\n",
       "                           learning_rate=0.1, loss='deviance', max_depth=3,\n",
       "                           max_features=None, max_leaf_nodes=None,\n",
       "                           min_impurity_decrease=0.0, min_impurity_split=None,\n",
       "                           min_samples_leaf=1, min_samples_split=2,\n",
       "                           min_weight_fraction_leaf=0.0, n_estimators=100,\n",
       "                           n_iter_no_change=None, presort='auto',\n",
       "                           random_state=None, subsample=1.0, tol=0.0001,\n",
       "                           validation_fraction=0.1, verbose=0,\n",
       "                           warm_start=False)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.ensemble import GradientBoostingClassifier\n",
    "gbm=GradientBoostingClassifier()\n",
    "gbm.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1\n",
    "y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.02),\n",
    "                     np.arange(y_min, y_max, 0.02))\n",
    "\n",
    "Z = gbm.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "Z = Z.reshape(xx.shape)\n",
    "cs = plt.contourf(xx, yy, Z, cmap=plt.cm.Paired)\n",
    "plt.scatter(X[:, 0], X[:, 1], marker='o', c=y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9422222222222222, 0.9422222222222222)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import metrics\n",
    "gbm.score(X,y),metrics.accuracy_score(y,gbm.predict(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import GridSearchCV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "d:\\pp\\Miniconda3\\envs\\pythonlearn\\lib\\site-packages\\sklearn\\model_selection\\_split.py:1978: FutureWarning: The default value of cv will change from 3 to 5 in version 0.22. Specify it explicitly to silence this warning.\n",
      "  warnings.warn(CV_WARNING, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "GridSearchCV(cv='warn', error_score='raise-deprecating',\n",
       "             estimator=GradientBoostingClassifier(criterion='friedman_mse',\n",
       "                                                  init=None, learning_rate=0.1,\n",
       "                                                  loss='deviance', max_depth=3,\n",
       "                                                  max_features=None,\n",
       "                                                  max_leaf_nodes=None,\n",
       "                                                  min_impurity_decrease=0.0,\n",
       "                                                  min_impurity_split=None,\n",
       "                                                  min_samples_leaf=1,\n",
       "                                                  min_samples_split=2,\n",
       "                                                  min_weight_fraction_leaf=0.0,\n",
       "                                                  n_estimators=100,\n",
       "                                                  n_iter_no_change=None,\n",
       "                                                  presort='auto',\n",
       "                                                  random_state=None,\n",
       "                                                  subsample=1.0, tol=0.0001,\n",
       "                                                  validation_fraction=0.1,\n",
       "                                                  verbose=0, warm_start=False),\n",
       "             iid='warn', n_jobs=None,\n",
       "             param_grid={'subsample': [0.6, 0.7, 0.75, 0.8, 0.85, 0.9, 1]},\n",
       "             pre_dispatch='2*n_jobs', refit=True, return_train_score=False,\n",
       "             scoring='accuracy', verbose=0)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gs=GridSearchCV(estimator=GradientBoostingClassifier(),scoring=\"accuracy\",param_grid={'subsample':[0.6,0.7,0.75,0.8,0.85,0.9,1]})\n",
    "gs.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "({'subsample': 0.7}, 0.8633333333333333)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gs.best_params_,gs.best_score_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9633333333333334"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gbm=GradientBoostingClassifier(subsample=.75)\n",
    "gbm.fit(X,y)\n",
    "metrics.accuracy_score(y,gbm.predict(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "d:\\pp\\Miniconda3\\envs\\pythonlearn\\lib\\site-packages\\sklearn\\model_selection\\_split.py:1978: FutureWarning: The default value of cv will change from 3 to 5 in version 0.22. Specify it explicitly to silence this warning.\n",
      "  warnings.warn(CV_WARNING, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "GridSearchCV(cv='warn', error_score='raise-deprecating',\n",
       "             estimator=GradientBoostingClassifier(criterion='friedman_mse',\n",
       "                                                  init=None, learning_rate=0.1,\n",
       "                                                  loss='deviance', max_depth=3,\n",
       "                                                  max_features=None,\n",
       "                                                  max_leaf_nodes=None,\n",
       "                                                  min_impurity_decrease=0.0,\n",
       "                                                  min_impurity_split=None,\n",
       "                                                  min_samples_leaf=1,\n",
       "                                                  min_samples_split=2,\n",
       "                                                  min_weight_fraction_leaf=0.0,\n",
       "                                                  n_estimators=100,\n",
       "                                                  n_iter_no_change=None,\n",
       "                                                  presort='auto',\n",
       "                                                  random_state=None,\n",
       "                                                  subsample=0.75, tol=0.0001,\n",
       "                                                  validation_fraction=0.1,\n",
       "                                                  verbose=0, warm_start=False),\n",
       "             iid='warn', n_jobs=None,\n",
       "             param_grid={'n_estimators': range(50, 121, 10)},\n",
       "             pre_dispatch='2*n_jobs', refit=True, return_train_score=False,\n",
       "             scoring='accuracy', verbose=0)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gs=GridSearchCV(estimator=GradientBoostingClassifier(subsample=.75),scoring=\"accuracy\",param_grid={'n_estimators':range(50,121,10)})\n",
    "gs.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "({'n_estimators': 110}, 0.8655555555555555)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gs.best_params_,gs.best_score_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9711111111111111"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gbm=GradientBoostingClassifier(subsample=.7,n_estimators=120)\n",
    "gbm.fit(X,y)\n",
    "metrics.accuracy_score(y,gbm.predict(X))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# xgboost\n",
    "## 概述\n",
    "Xgboost是GBDT算法的高效实现，有效应用了数值优化，损失函数更复杂。目标函数依然是所有树的预测值相加等于预测值。\n",
    "\n",
    "总体来说，xgboost相比于gbdt的有很多创新之处：\n",
    "1. 传统GBDT以CART作为基分类器，xgboost还支持线性分类器，这个时候xgboost相当于带L1和L2正则化项的逻辑斯蒂回归（分类问题）或者线性回归（回归问题）。\n",
    "2. 传统GBDT在优化时只用到一阶导数信息，xgboost则对代价函数进行了二阶泰勒展开，同时用到了一阶和二阶导数（xgboost工具支持自定义代价函数，只要函数可一阶和二阶求导。）\n",
    "3. xgboost在代价函数里加入了正则项，用于控制模型的复杂度。正则项里包含了树的叶子节点个数、每个叶子节点上输出的score的L2模的平方和。从方差和偏差的角度来讲，正则项降低了模型的偏差，使学习出来的模型更加简单，防止过拟合，这也是xgboost优于传统GBDT的一个特性。\n",
    "4. Shrinkage（缩减），相当于学习速率（xgboost中的eta）。每次迭代，增加新的模型，在前面乘以一个小于1的系数，降低优化的速度，这样每次走一小步逐步逼近最优模型比每次走一大步逼近更加容易避免过拟合现象；\n",
    "5. 列抽样（column subsampling）。xgboost借鉴了随机森林的做法，支持列抽样（即每次的输入特征不是全部特征），不仅能降低过拟合，还能减少计算，这也是xgboost异于传统gbdt的一个特性。\n",
    "6. 忽略缺失值：在寻找splitpoint的时候，不会对该特征为missing的样本进行遍历统计，只对该列特征值为non-missing的样本上对应的特征值进行遍历，通过这个工程技巧来减少了为稀疏离散特征寻找splitpoint的时间开销；\n",
    "7. 指定缺失值的分隔方向：可以为缺失值或者指定的值指定分支的默认方向，为了保证完备性，会分别处理将missing该特征值的样本分配到左叶子结点和右叶子结点的两种情形，分到那个子节点带来的增益大，默认的方向就是哪个子节点，这能大大提升算法的效率。\n",
    "8. 并行化处理：在训练之前，预先对每个特征内部进行了排序找出候选切割点，然后保存为block结构，后面的迭代中重复地使用这个结构，大大减小计算量。在进行节点的分裂时，需要计算每个特征的增益，最终选增益最大的那个特征去做分裂，那么各个特征的增益计算就可以开多线程进行，即在不同的特征属性上采用多线程并行方式寻找最佳分割点。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 案例\n",
    "注意：xgboost没有在sklearn中的实现，需要安装：pip install xgboost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "from xgboost import XGBClassifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "XGBClassifier(base_score=0.5, booster='gbtree', colsample_bylevel=1,\n",
       "              colsample_bytree=1, gamma=0, learning_rate=0.1, max_delta_step=0,\n",
       "              max_depth=3, min_child_weight=1, missing=None, n_estimators=100,\n",
       "              n_jobs=1, nthread=None, objective='binary:logistic',\n",
       "              random_state=0, reg_alpha=0, reg_lambda=1, scale_pos_weight=1,\n",
       "              seed=None, silent=True, subsample=1)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xgb=XGBClassifier()\n",
    "xgb.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1\n",
    "y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.02),\n",
    "                     np.arange(y_min, y_max, 0.02))\n",
    "\n",
    "Z = xgb.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "Z = Z.reshape(xx.shape)\n",
    "cs = plt.contourf(xx, yy, Z, cmap=plt.cm.Paired)\n",
    "plt.scatter(X[:, 0], X[:, 1], marker='o', c=y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9355555555555556"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xgb.score(X,y)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {
    "height": "398.97px",
    "width": "409.931px"
   },
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
